1. FIELD OF THE INVENTION
This invention relates to analog to digital convertors, and particularly to such convertors where an angle representing the phase difference between two electronic signals is digitized.
2. RELATED ART
In analog to digital conversion, the Nyquist criteria requires one to sample at a rate which is at least twice that of the highest frequency of the analog input signal. In order to reduce the sampling rate, for a limited bandwidth signal, the analog signal can first be translated to a lower frequency range by mixing with a local oscillator without loss of information. This process is called down conversion, and a down converted signal that meets the Nyquist criteria retains both amplitude and phase information. An early phase digitization technique was 1 bit digitization. This technique retained the phase information by squaring the incoming signal at the expense of the amplitude information.
Whether down converted or not, in digitizing the analog signal, fourier analysis of the digital waveform shows that in 1 bit digitization, harmonics of the sampling frequency are generated, but with an amplitude reduced by a factor of 1/m of that of the fundamental frequency, where m represents the odd integers from one to infinity and represents multiples of the sampling frequency.
If the analog signal is subsequentially reconstructed from the digitized data, the undesired harmonics introduced by the sampling process are retained. In many applications these harmonics are of no concern due to their reduced amplitude. But for certain applications, the near-in harmonics have sufficient amplitude to cause difficulties.
U.S. Pat. No. 4,277,748 to Gerst, et al. (Gerst) improved harmonic rejection by the use of a phase angle digitizer. A signal .theta. representative of the phase differences between an input signal and a reference signal is provided. In-phase (I or sin .theta.) and quadrature (Q or cos .theta.) signals are generated and fed to "orthogonal" inputs of a bridge circuit. A signal representing the vector sum of sin .theta. and cos .theta. moves around the bridge in response to the instantaneous value of .theta.. The range of .theta. (i.e. 2.pi. radians in phase space) is segmented by tapping the bridge at points representing various angles in phase space. All values of .theta. are available, i.e. phase space in spanned.
Pairs of tapped signals are input to digital comparators to generate a digital signal for each segment in phase space at a given time. Knowing the digital value of .theta. at each segment in phase space at a given time, is sufficient to uniquely determine the phase state of .theta..
Gerst's device divides phase space into equal segments and outputs a digital bit for each segment. For sixteen segments of 22.5.degree. each, Gerst employs eight comparators and translates the outputs of eight comparators to a four bit signal (the number of bits needed to uniquely identify .theta. given sixteen phase segments. Gerst's approach results in a reduction (i.e. rejection) in amplitude of odd harmonics 3, 5, 11 and 13 below the 1/m factor of the 1 bit digitization scheme, but the amplitude of odd harmonics 7, 9, 15 and 17 still obeys the 1/m scaling rule.
If a three bit signal were employed, the map and time waveform of FIGS. 1a and 1b represent Gerst's phase digitization scheme. Note that eight phase state are possible, each spanning 45.degree. in phase space. Note also that there are only five amplitude states associated with these eight phase states, with all states being unambiguous in phase but three pairs of the states (i.e. states 1, and 3, states 4 and 8, and states 5 and 7) being ambiguous in amplitude.
It is desirable to reduce the number of bits required to achieve a given level of harmonic rejection in digitizers as compared to Gerst and others, or alternatively, improve harmonic rejection for a given number of bits.